The concept of exponential
attenuation is relevant primarily to uncharged ionizing radiation (i.e.,
photons and neutrons), which lose their energy in relatively few large
interactions, rather than charged particles which typically undergo many small
collisions, losing their kinetic energy gradually. An individual uncharged particle has a
significant probability of passing straight through a thick layer of matter
without losing any energy, while a charged particle must always lose some or
all of its energy.

An uncharged particle has no
limiting “range” through matter, beyond which it cannot go; charged particles
all encounter such a range limit as they run out of kinetic energy. For comparable energies, uncharged particles
penetrate much farther through matter, on the average, than charged particles,
although this difference gradually decreases at energies above 1 MeV. Consider a
monoenergetic parallel beam consisting of a very large number N0
of uncharged particles incident perpendicularly on a flat plate of material of
thickness L

Simple Exponential Attenuation:

•
Assume for
this ideal case that each particle either is completely absorbed in a single
interaction, producing no secondary radiation, or passes straight through the
entire plate unchanged in energy or direction

•
Let (m×1) be the probability that an individual
particle interacts in a unit thickness of material traversed

•
The
probability that it will interact in an infinitesimal thickness dl is mdl

•
If N
particles are incident upon dl, the change dN in the number N
due to absorption is given by

dN = -µdl

where
m is typically
given in units of cm-1 or m-1, and dl is
correspondingly in cm or m

•
The
fractional change in N due to absorption of particles in dl is
just

dN/N = -µdl

•
Integrating
over the depth l from 0 to L, and corresponding particle
populations from N0 to NL, give

•
This is
the law of exponential attenuation, which applies either for the ideal case
described above (simple absorption, no scattering or secondary radiation), or
where scattered and secondary particles may be produced but are not counted
in NL

•
The
quantity m is called the linear
attenuation coefficient, or simply the attenuation coefficient

•
When it is
divided by the density r of the attenuating medium, the mass attenuation coefficientm/r (cm2/g or m2/kg) is obtained

•
m is sometimes referred to as the “narrow-beam attenuation coefficient”